THE HYPERCYCLE — a dart

THE HYPERCYCLE replicators helping replicators

Eigen’s answer to how information survives before enzymes are accurate: link self-replicators in a cycle, each one catalyzing the replication of the next, the last closing back to the first. This second-order coupling grows hyperbolically and lets a set of short molecules carry more information together than any could alone — a way past the error threshold. The bridge between chemistry and the first genomes.

THE TECHNIQUE cyclic coupling: i catalyzes i+1, closing

The demo builds a 4-member hypercycle where each replicator catalyzes the next and the cycle closes: live demo

HISTORY & CREDIT Eigen & Schuster · 1977

“Hypercycle and autocatalytic set are the same.” — a hypercycle couples self-replicators (second-order), while an autocatalytic set needs no individual replicator; distinct ideas. cited

the coupling · replicator i catalyzes the replication of i+1.
the closure · the last feeds the first — the cycle closes, growth turns hyperbolic.
1977 · Manfred Eigen & Peter Schuster — a route past the error threshold.

Together, short molecules carry a long message. origin of life

RECOMMEND FOR I-13 the cycle, on the compiler

On i-13, a 4-member cycle closes (3→0) with each replicator helping the next:

$ i13 run lf_hypercycle.i13 RUN OK · 69 step(s) cycle_closes = 1 -- 0->1->2->3->0 each_helps_next = 1 second_order = 1

Recommend as a NULL — a cyclic fixed structure (B43/B39). The coupling cycle is a pinned graph; every correct check finds the same closure. Distinct from the autocatalytic set but the same gate. NULL — replicators helping replicators.